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arXiv:1809.11134

Quantum Encoded Quantum Evolutionary Algorithm for the Design of Quantum Circuits

Georgiy Krylov, Martin Lukáč

Published Sep 28, 2018• 0 citations
arXivHTMLPDF

Abstract

In this paper we present Quanrum Encoded Quantum Evolutionary Algorithm (QEQEA) and compare its performance against a a classical GPU accelerated Genetic Algorithm (GPUGA). The proposed QEQEA differs from existing quantum evolutionary algorithms in several points: representation of candidates circuits is using qubits and qutrits and the proposed evolutionary operators can in theory be implemented on quantum computer provided a classical control exists. The synthesized circuits are obtained by a set of measurements performed on the encoding units of quantum representation. Both algorithms are accelerated in GPGPU. The main target of this paper, is not to propose a completely novel quantum genetic algorithm but to rather experimentally estimate the advantages of certain components of genetic algorithm being encoded and implemented in a quantum compatible manner. The algorithms are compared and evaluated on several reversible and quantum circuits. The results demonstrate that on one hand the quantum encoding and quantum implementation compatible implementation provides certain disadvantages with respect to the classical evolutionary computation. On the other hand, encoding certain components in a quantum compatible manner could in theory allow to accelerate the search. This acceleration would in turn counter weight the implementation limitations.

DOI
10.48550/arxiv.1809.11134

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In this paper we present Quanrum Encoded Quantum Evolutionary Algorithm (QEQEA) and compare its performance against a a classical GPU accelerated Genetic Algorithm (GPUGA). The proposed QEQEA differs from existing quantum evolutionary algorithms in several points: representation of candidates circuits is using qubits and qutrits and the proposed evolutionary operators can in theory be implemented on quantum computer provided a classical control exists. The synthesized circuits are obtained by a set of measurements performed on the encoding units of quantum representation. Both algorithms are accelerated in GPGPU. The main target of this paper, is not to propose a completely novel quantum genetic algorithm but to rather experimentally estimate the advantages of certain components of genetic algorithm being encoded and implemented in a quantum compatible manner. The algorithms are compared and evaluated on several reversible and quantum circuits. The results demonstrate that on one hand the quantum encoding and quantum implementation compatible implementation provides certain disadvantages with respect to the classical evolutionary computation. On the other hand, encoding certain components in a quantum compatible manner could in theory allow to accelerate the search. This acceleration would in turn counter weight the implementation limitations.
In this paper we present Quanrum Encoded Quantum Evolutionary Algorithm (QEQEA) and compare its performance against a a classical GPU accelerated Genetic Algorithm (GPUGA). The proposed QEQEA differs from existing quantum evolutionary algorithms in several points: representation of candidates circuits is using qubits and qutrits and the proposed evolutionary operators can theoretically be implemented on quantum computer provided a classical control exists. The synthesized circuits are obtained by a set of measurements performed on the encoding units of quantum representation. Both algorithms are accelerated using (general purpose graphic processing unit) GPGPU. The main target of this paper is not to propose a completely novel quantum genetic algorithm but to rather experimentally estimate the advantages of certain components of genetic algorithm being encoded and implemented in a quantum compatible manner. The algorithms are compared and evaluated on several reversible and quantum circuits. The results demonstrate that on one hand the quantum encoding and quantum implementation compatible implementation provides certain disadvantages with respect to the classical evolutionary computation. On the other hand, encoding certain components in a quantum compatible manner could in theory allow to accelerate the search by providing small overhead when built in quantum computer. Therefore acceleration would in turn counter weight the implementation limitations.
In this work we present a comparative study of several GPU accelerated elements of a Genetic Algorithm (GA) for the synthesis of quantum circuits on the level of Electro-Magnetic (EM) pulses. The novelty in our approach is in the implementation: a) a completely GPU accelerated quantum simulator, b) GPU accelerated genetic operators and fitness evaluation and finally c) a set of GPU implemented optimizations for GPU accelerated evolutionary search optimization for the synthesis of quantum circuits. The reason for using EM pulses model for synthesis is the observation that this model requires the largest amount of elementary rotations to implement quantumlogic gates and thus provides a good measure to evaluate the efficiency of the acceleration by the GPU processor. The reason to use a GA is the advantage of pseudo evolutionary search in very large problem space such as the one defined by the Ising model where the EM realized quantum circuits are evolved. As a result of the several GPU optimizations several new circuits implementations are presented and their cost is compared to thecurrently known Ising model implementations.
Recently, researchers have applied genetic algorithms (GAs) to address some problems in quantum computation. Also, there has been some works in the designing of genetic algorithms based on quantum theoretical concepts and techniques. The so called Quantum Evolutionary Programming has two major sub-areas: Quantum Inspired Genetic Algorithms (QIGAs) and Quantum Genetic Algorithms (QGAs). The former adopts qubit chromosomes as representations and employs quantum gates for the search of the best solution. The later tries to solve a key question in this field: what GAs will look like as an implementation on quantum hardware? As we shall see, there is not a complete answer for this question. An important point for QGAs is to build a quantum algorithm that takes advantage of both the GA and quantum computing parallelism as well as true randomness provided by quantum computers. In the first part of this paper we present a survey of the main works in GAs plus quantum computing including also our works in this area. Henceforth, we review some basic concepts in quantum computation and GAs and emphasize their inherent parallelism. Next, we review the application of GAs for learning quantum operators and circuit design. Then, quantum evolutionary programming is considered. Finally, we present our current research in this field and some perspectives.
Automatic quantum circuit design is motivated by the difficulties in manual design, because quantum algorithms are highly non-intuitive and practical quantum computer hardware is not yet available. Thus, quantum computers have to be simulated on classical hardware which naturally entails an exponential growth of computational costs and allows only to simulate small quantum systems, i. e., with only few qubits. Huge search spaces render evolutionary approaches nearly unable to achieve breakthrough solutions in the development of new quantum algorithms. Consequently, at present we must be content to evolve essentially already existing (black-box) quantum algorithms. This thesis presents empirical results on the evolution of quantum circuits using genetic programming. For that purpose, a linear and a linear-tree GP system (allowing intermediate measurements) with integrated quantum computer simulator were implemented. Their practicality in evolving quantum circuits is shown in different experiments for 1-SAT (solutions act like Hogg's algorithm) and the Deutsch-Jozsa problem. These experiments confirm that the evolution of quantum circuits is practically feasible only for sufficiently small problem instances. In this context, scalability and the detection of scalability becomes very important. It is shown that scalable quantum circuits are evolvable to a certain degree: a general quantum circuit can be inferred manually from the evolved solutions for small instances of the given problem. Besides, further experiments indicate that 're-evolution' is effective for the evolution of scalable quantum circuits. With this method the start population of a problem instance is inoculated with evolved solutions for a smaller problem instance. Furthermore, investigations of fitness landscapes and selection strategies are made, with the aim of improving the efficiency of evolutionary search. A notable result is that using the crossover operator damages rather than benefits evolution of quantum circuits.
Designing efficient quantum circuits that leverage quantum advantage compared to classical computing has become increasingly critical. Genetic algorithms have shown potential in generating such circuits through artificial evolution. However, integrating quantum advantage into the fitness function of these algorithms remains unexplored. In this paper, we aim to enhance the efficiency of quantum circuit design by proposing two novel approaches for incorporating quantum advantage metrics into the fitness function of genetic algorithms.1 We evaluate our approaches based on the Bernstein-Vazirani Problem and the Unstructured Database Search Problem as test cases. The results demonstrate that our approaches not only improve the convergence speed of the genetic algorithm but also produce circuits comparable to expert-designed solutions. Our findings suggest that automated quantum circuit design using genetic algorithms that incorporate a measure of quantum advantage is a promising approach to accelerating the development of quantum algorithms.
It has been experimentally proven that realizing universal quantum gates using higher-radices logic is practically and technologically possible. We developed a Parallel Genetic Algorithm that synthesizes Boolean reversible circuits realized with a variety of quantum gates on qudits with various radices. In order to allow synthesizing circuits of medium sizes in the higher radix quantum space we performed the experiments using a GPU accelerated Genetic Algorithm. Using the accelerated GA we compare heuristic improvements to the mutation process based on cost minimization, on the adaptive cost of the primitives and improvements due to Baldwinian vs. Lamarckian GA. We also describe various fitness function formulations that allowed for various realizations of well known universal Boolean reversible or quantum-probabilistic circuits.